Vector generator utilizing an exponential analogue output signal

ABSTRACT

An improved vector generating electrical system is provided for forming the mathematical representation of a vector. The system is particularly useful for drawing images in any desired pattern on the screen of a cathode-ray tube, whereby the images are composed of a multitude of vector lines having horizontal and vertical components. With the improved system of the invention, the vector drawing speed is not constant, but is an exponential function. One embodiment utilizes suitable switching gates to adjust the time constant of the exponential function at discrete points during the drawing stroke to reduce the vector drawing time as much as possible. In a second embodiment the time constant is changed in an infinite resolution system.

I United States Patent 1191 1111 3,77 Hasenbalg 1 Nov. 13, 1973 VECTORGENERATOR UTILIZING AN 1 ,384 2113 011; g g 19s 39 l 1 ra o 197 gfc gilANALOGUE OUTPUT 3,333,147 7/1967 Henderson.... 315/23 X 3,716,749 2/1973Colby et a1. 315/23 inventor: Ralph D. Hasenbalg, Canoga Park,

Calif.

Assignee: Vector General Inc., Canoga Park,

Calif.

Filed: Nov. 9, 1972 Appl. No.: 304,942

Related 1.1.8. Application Data Continuation-impart of Ser. No. 95,515,Dec. 7, I970, abandoned.

US. Cl. 315/23, 315/25, 315/26, 235/198 Field of Search H01j/29/70;315/23, 315/24, 25, 26; 235/197, 198

References Cited UNITED STATES PATENTS 11/1959 Mollen et a1 315/24 X10/1960 Roppel 315/23 X 12/1964 Brouillette, Jr. et a1 235/198 9/1969Brouillette, Jr. et a1 315/24 X 1/1971 Tong 235/197 X PrimaryExaminer-Benjamin R. Padgett Assistant Examiner-P. A. NelsonAttorney-Robert Louis F inkel [57] ABSTRACT An improved vectorgenerating electrical system is provided for forming the mathematicalrepresentation of a vector. The system is particu1arly useful fordrawing images in any desired pattern on the screen of a cathode-raytube, whereby the images are composed of a multitude of vector lineshaving horizontal and vertical components. With the improved system ofthe invention, the vector drawing speed is not constant, but is anexponential function. One embodiment utilizes suitable switching gatesto adjust the time constant of the exponential function at discretepoints during the drawing stroke to reduce the vector drawing time asmuch as possible. In a second embodiment the time constant is changed inan infinite resolution system.

9 Claims, 11 Drawing; Figures PAIENIEBuuv 13 ms SHEET 2 OF 6 3,772,563

VECTOR GENERATOR UTILIZING AN EXPONENTIAL ANALOGUE OUTPUT SIGNAL Thisapplication is a continuation-in-part of copending application Ser. No.95,515 filed in the name of Ralph D. Hasenbalg on Dec. 7, 1970, and nowabandoned.

BACKGROUND OF THE INVENTION Cathode-ray tube circuits have been wellknown for many years for the graphic display of electrically computedinformation. Basically, in a cathode-ray tube, a stream of electrons isdirected from an electron gun past two pairs of electrostatic deflectionplates or electromagnetic deflection coils towards a phosphorizedscreen. The point at which the electron beam formed by the stream ofelectrons impinges on the screen is temporarily illuminated. The twopairs of deflection plates or coils control the position of theresulting illuminated spot on the screen. The deflection of theilluminated spot from the center of the screen depends upon themagnitude of the voltage applied across the deflection plates, or coils.One pair of deflection plates, or coils, controls the deflection of theelectron beam vertically in the Y-direction, and the other pair ofplates, or coils, controls the deflection horizontally in theX-direction. Simultaneously, the two pairs of plates, or coils, candirect the electron beam to impinge on any point within the range of thescreen, and predetermined voltage levels across the horizontal andvertical deflection plates correspond to definite X- and Y- coordinatepositions of the illuminated spot on the screen.

The representation of a vector on the aforesaid phosphorized screen ofthe cathode-ray tube, and which has a definite starting point and endpoint, is accomplished by varying the voltage levels between the valuescorresponding to the aforesaid starting and end points in a rapidrepetitive sequence, so that the illuminated spot moves rapidly betweenthe two points. Because of the persistence of vision of the human eye,the moving spot creates the image of a line insofar as the eye isconcerned. It becomes obvious, thereofore, that in order to create areasonably accurate presentation of a desired vector, the shape of thevoltage pulses across the horizontal and vertical deflection plates, orcoils, and the phased timing of these pulses with respect to oneanother, have to be precisely controlled. Otherwise, a distortion of theline from the desired image would result.

One commonly used method of the prior art to achieve such a control iscarried out as follows. Assuming the location of the vector origin pointat coordinate X Y and of the vector end points at coordinate X Y thelength of the vector R is first computed according to the equation:

The aforesaid computation can be accomplished by applying the givenquantities to an analog-to-digital converter, performing the calculationby digital meth ods to the desired degree of precision, and by thenrestoring the result to analog form by a digital-to-analog converter.From the length R of the vector, the time T(R) to draw the vector isalso computed. The time in terval T(R) is a function of the length R ofthe vector and of the speed of the moving illuminated spot, the latterbeing governed by the required intensity of illumination.

Next, in accordance with the prior art method, the coordinate positionsof the moving spot as a function of time t are determined, according tothe following equations:

(X X T(R) t+X y(t)=[ (Y Y )/T(R) -t+ Y The aforesaid computations areaccomplished by computing circuits using a ramp function, whereby theslope and linearity of the ramp must be accurately controlled. Itbecomes apparent to those skilled in the art that the computing circuitsinvolved in the aforesaid prior art method, and which includedigital-to-analog and analog-to-digital converters, digital computers,and precision ramp function generators, involve a considerable number ofcircuit components with precisely controlled values; and that such priorart circuits further require provisions for calibrations and adjustmentsto compensate for unavoidable variations in component values, and forchanges of component values under the influence of time and environment.

Unlike the prior art system referred to above, which requires thecontrol of several separate parameters to a high degree of precision,the improved system of the present invention requires the accuratecontrol of only one parameter, namely, the matching of two timeconstants in an exponential voltage rise function. This parameter in thesystem of the invention governs the ratio between the horizontal andvertical components of the vector being drawn. In addition, the systemof the present invention can be constructed with fewer and lessexpensive components than the prior art system, and it requires fewercalibrations and adjustments.

A principal objective of the present invention, therefore, is to providean improved system capable of representing vectors in an improvedmanner, as compared with the prior art systems. This is achieved in thesystem of the invention by accurately controlling but a singlecomputation parameter and by the use of considerably fewer componentsthan the aforesaid prior art system. Moreover, the system of theinvention has fewer calibration requirements than the prior art system.

The invention provides a vector generator to generate a straight linefrom one point to another point on the viewing surface of a cathode-raytube. The vector generator holds the previous input point and generatesa straight line between that point and the new input point. Three inputsto the cathode-ray tube system are required: one for horizontaldeflection, one for vertical deflection and the third for intensitycontrol. In prior art vector generators, as described above, the vectorsare drawn after all of the vector parameters are first computed, andseveral steps are required. First, the difference between the presentand the previous input vector endpoints must be obtained for both thehorizontal and vertical deflection. Second, the time to draw the vector,the required velocity in both the horizontal and vertical directions andthe intensity level must be selected. Third, the vector is drawn usingthe parameters selected. The vector drawing spot arrives at the newpoint within the accuracy of the several computations required. Toinsure accurate vector endpoints the endpoint difference computation,the drawing rate, and the drawing time must all be highly accurate inthe prior art system. Specifically, an accuracy of 0.1 percent isgenerally necessary for good visual appearance. Precision intensitylevel is not necessary, because as much as percent change cannot bedetected by the eye.

The concept used by the vector generators of the in vention reduces theprecision requirements and cost. Vector drawing time is also reducedbecause less computation at lower accuracy is required to generate avector visually as acceptable as the prior art.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 5 is a time-voltage diagram,illustrating the changes in the effective time constant during a vectorstroke, in the operation of the system of the invention;

FIG. 6 is a block diagram of a second embodiment of the invention;

FIG. 7 is a series of curves useful in explaining the operation of theembodiment of FIG. 6; and

FIGS. 8-11 are circuit diagrams of certain of the blocks of FIG. 6.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS Referring now toFIGS. 1-5 of the drawings, wherein like characters designate like orcorresponding parts, there is illustrated in FIG. 1 a schematic diagramof a typical cathode-ray tube 10. At the face of the cathoderay tube 10there is a phosphorized screen 12, on which an electron beam 14 is madeto impinge. The electron beam 14 passes between a pair of verticaldeflection plates 16, and a pair of horizontal deflection plates 18. Thevoltage across the vertical deflection plates 16 is controlled by theY-axis control circuits 42, while the voltage across the horizontaldeflection plates is controlled by the X-axis control circuits 44.

The electron beam 14 emerges from an electron gun 38, the detailedconstruction of which varies with the various cathode-ray tubemanufacturers. In most cases, the electron gun 38 contains a filament20, a heated cathode 30, a control grid 32, an isolating electrode 34,and an accelerating electrode 36. The filament is supplied with electriccurrent from an alternating current power supply 22. A direct currentpower supply and control circuits for the various electrodes of the gunare represented by the block 40. The detailed construction of the powersupply circuits 22 and 40 is well known to those skilled in the art and,for that reason, will not be described in detail herein. The followingdiscussion will relate primarily to the X-axis and Y-axis deflectioncontrol circuits 42 and 44.

Referring now to the vector diagram shown in FIG. 2,-the starting pointof the vector is given by'the coordinates X and Y while the end point isgiven by the coordinates X and Y The illuminated spot on thephosphorized screen 12 of the cathode-ray tube of FIG. 1 is movedbetween the starting point and the end point in repetitive cycles inorder to trace out the vector. The interval of travel of the spotbetween the starting and end points within one single cycle willhereinafter be defined as one vector stroke. The end point of one vectormay serve as the starting point for a succeeding vector.

If the illuminated spot is controlled to trace the path of a straightline, it is necessary that at any instant t the coordinates x(t) andy(t) conform to the relation:

For a better understanding of the basic principles involved in thepractice of the present invention, a simplified version of adeflectioncontrol circuit is shown in FIG. 3. Since the samemathematical principles are involved in a construction of the Y-axis andX-axis deflection control circuits 42 and 44, expressions for voltagesare substituted in conjunction with the circuit of FIG. 3, and in thefollowing mathematical analysis for the expressions containing thecoordinate points.

The simplified deflection control circuit of FIG. 3 may be included, forexample, in the Y-axis deflection control circuit 42, or in the X-axisdeflection control circuit 44 of FIG. 1. The simplified circuit of FIG.3 includes an input terminal designated V (t) which is connected to aresistor R16. The resistor R16 is connected to the positive inputterminal of an operational amplifier A12. The negative input terminal ofthe operational amplifier A12 is connected to a grounded resistor R25.The output terminal of the operational amplifier designated V (t) isconnected back to the negative input terminal through a resistor R24,and is also connected through a resistor R23 to the negative inputterminal of an integrating operational amplifier A3. The positive inputterminal of the operational amplifier A3 is grounded. The outputterminal of the operational amplifier A3 is coupled back to the negativeinput terminal through a capacitor C5, and is connected through aresistor R17 to the positive input terminal of the operational amplifierA12. The output of the operational amplifier A3 is connected to anoutput terminal designated V (t).

In the circuit shown in FIG. 3, the input voltage applied to the inputterminal V,(t) is a step function corresponding to the expression (Y Y,)or (X X in equation (3). The voltage at the output terminal V (t) mayrepresent the expression (Y y(t)) or (X x(t)) in equation (3). It can beshown from the basic theory of operational amplifiers that the voltageappearing at the output terminal V (t) of the operational amplifier A12may be defined by the equation:

lates the voltages V (t) and V (t) by the integral expression:

If the values for the resistors R16 and R17 are made equal, then thefollowing expression for the error voltage may be obtained:

6 [V (t) V (t)/2] Substituting the expression for e of equation (6) intoequation (4), the following expression is obtained:

Replacing the expression for V (t) of equation (7) in equation thefollowing expression is obtained:

The expression outside the integral sign of equation (8) can be lumpedinto a single constant whose value is determined by the values of theresistors R23, R24 and R25, and of the capacitor C5. That constant maybe indicated as l/T Further development of equation (8) then yields theintegral equation:

V is a step function, so that V may be substituted for the value V attime zero, and V may be substituted for the value V after time zero. ByLaplace transformation, the solution to equation (9) is as follows:

If the voltage levels are now translated back into the expressions forthe X- and Y-coordinates, the following equations are obtained for thevertical and horizontal deflection control circuits respectively:

(lla) [X X(t)] (X X,)e 1

If the ratio between the expression (1 la) and (11a) is taken, therelation shown in equation (3) is obtained. As long as the time constantT is the same for the vertical and horizontal deflection controlcircuits, the exponential terms in the ratio cancel out, and the spot onthe screen will follow a straight line, although the voltage in eachdeflection control circuit is an exponential function of time.

Thus, it is obvious that in order to obtain an accurate trace of thevector on the screen in the system of the invention it is only. requiredto match the component values in the vertical and horizontal deflectioncircuits.

This task is considerably easier and less complex than the multipleadjustments and calibrations required in the prior art system. Inaddition, the system of the present invention avoids the necessity offabricating expensive and complicated computing circuits,digital-toanalog converters, and the like, such as are used in the priorart systems.

Reference is now made to the system of FIG. 4, which is a representationof the system of FIG. 3 in greater detail. In the system of FIG. 4, apair of operational amplifiers A1 and A2 replaces the operationalamplifier A12 of FIG. 3.

The input terminal of the circuit of FIG. 4, which is designated X isconnected to a pair of resistors R16 and R18 which, in turn, areconnected respectively to feedback resistors R17 and R19. The junctionof the resistors R18 and R19 is connected to appropriate time constantcontrol circuits designated by the block 100. The junction of theresistors R16 and R17 is connected to the positive input terminal of theoperational amplifier A1. The output of the operational amplifier Al isconnected to the positive input terminal of the operational amplifier A2whose output is connected to the junction of a pair of resistors R5 andR8. The output terminal of the operational amplifier A1 is connected toa feedback resistor R1 which, in turn, is connected back to the negativeinput terminal of the operational amplifier, as in FIG. 3.

The grounded resistor R25 of FIG. 3 is replaced by a pair of resistorsR1 and R2 which are selectively switched into the circuit by gatesformed by the field effect transistors Q6 and Q12, these beingcontrolled by the time constant control circuits when predeterminedlevels are reached by the deflection voltages. Likewise, the output ofthe operational amplifier A2 is connected back to the negative inputthrough a resistor R5. This latter resistor is connected to resistorsR4, R6 and R7, these being selectively switched into the circuit bygates formed by the field effect transistors Q18, Q23 and Q29, likewiseunder the control of the time constant control circuit 100. The resistorR23 of FIG. 3 is replaced by resistors R8, R10 and R11, and by apotentiometer R12, connected as shown. These elements are switched inand out of the circuit by switches such as field effect transistors Q35,Q54 and Q55. These latter transistors are also controlled by circuits inthe block 100.

As is well known, a parallel-series combination of a multiplicity ofresistors can yield various distinct values for a net effectiveresistance, depending on which of the resistors are connected ordisconnected into or from a particular circuit. In the circuit shown inFIG. 4, the combination of resistors R1 through R12, and the operationalamplifiers Al and A2, replace the resistors R23, R24, R25 and theoperational amplifier A12 of the circuit shown in FIG. 3, :as mentionedabove. Then, by selectively operating the switching gates formed by thefield effect transistors Q6, Q12, Q18, A23, Q29, a variety of differentoverall resistance values may be obtained which, in turn, influence theeffective time constant of the deflection control circuits 42 or 44, inwhich the circuitry is incorporated. As mentioned above, the fieldeffect transistors Q6, Q12, Q18, Q23 and Q29 are controlled by the timeconstant control circuits 100, to be selectively actuated whenpredetermined voltage levels are reached.

The purpose of changing the effective time constant of the deflectioncircuits during the vector stroke is made clear by reference to thecurve of FIG. 5. In the diagram of FIG. 5, the difference between thevoltage across the corresponding deflection plates of the cathode-raytube at any given instant t, and the desired end pont voltage is plottedas an expotential function, originally with the starting time constant TIf the same time constant T were to be maintained for the entire vectorstroke, the time to reach an acceptable end point error voltage EPEwould take too long, as may be deduced from the path of the extension ofthe initial curve shown as a broken line in FIG. 5. At a givenpredetermined switching voltage level V one or more of the field effecttransistors Q6, Q12, Q18, O23, O29 is actuated so that a new timeconstant T, becomes effective. This new time constant T, governs thevoltagetime relationship until the next voltage switching level V 2 isreached, creating a new time constant T Although only two distinctswitching voltage levels are shown in the diagram of FIG. 5 in order tofacilitate the explanation of the system, it is apparent that with aselected number of switching gates, a corresponding number of differenttime constants may be derived. Therefore, the average slope of thevoltage-time curve, which at the same time represents the velocity ofthe illuminated spot across the screen 12 of the cathoderay tube of FIG.1, can be controlled, with the speed being increased when the end pointerror voltage EPE has been reduced to an acceptable level.

Assuming the circuit of FIG. 4 is incorporated into the X-axisdeflection control circuit 44, it will be understood that the block 100also includes time constant control circuits which simultaneouslyactuate corresponding field effect transistors, or other switchingdevices, in a similar circuit in the Y-axis deflection control circuit42, so that the identical time constant is used in both the X-axis andY-axis deflection control circuits at any instant. In this way, theconstant ratio between the horizontal and vertical component of thevector is maintained according to the relationship set out in equation(3).

As the curve in FIG. 5 approaches the point of acceptable end pointerror voltage EPE, the slope of the curve also approaches azero valuewhich tends to produce an asymptotic relationship. This slope, representing the trace velocity is given by the expression dV,(t)/dt. Referringagain to equation (5 we note that a differential of both sides of theequation yields the equation:

: ''''l/C5'Rg3 Thus, by simply monitoring the voltage level at V,(t), itis possible to determine when the trace velocity has reached thepredetermined minimum acceptable level, and when the end point has beenreached within the limits of the desired accuracy. This represents adistinct advantage over the prior art systems, in which complexcomputations are made by complex circuitry to determine the end point ofthe vector.

In the system of the invention, as soon as the value of V,(t) hasreached the minimum acceptable level, the end point signal is generatedsimultaneously closing the switching circuit of the field effecttransistor Q35, and opening the switching circuit of the transistor Q55.

Thus, the capacitor C5 remains charged, and the volage V (t) ismaintained at a constant level until the drawing of the next vector isinitiated. In this way, the end point of the present vec-tor serves asthe starting point for the next succeeding vector.

As the slope of the curve in FIG. 5 changes at the various switchingpoints, the speed at which the cathoderay beam is swept across thescreen changes, so that the illumination intensity of the spot alsochanges. However, since the average slope of the curve is held withinreasonable limits during the trace of the vector, the variation inillumination intensity is not serious. This variation can be easily heldto within 10 percent, and such intensity fluctuation does not seriouslyaffect the image observed by the human eye. Appropriate controls may beintroduced from the time constant control circuits to the DC powersupply 40 of FIG. 1 to compensate for the changes in illuminationintensity, if so desired, for example, control circuits of the typedescribed in US. Pat. No. 2,860,284 may be used for this purpose. In anyevent, it is the position of the illuminated spot at any instant of thetrace which is the critical parameter, and which is precisely controlledby the system of the invention.

In the embodiment of FIG. 4 the time constant is switched at discretepoints as described above. In the embodiment of FIG. 6, however, thetime constant changes in an infinite resolution system which may belikened to that of replacing a switched attenuator with a potentiometer.FIG. 6 is a simplified block diagram of the second embodiment.

The system of FIG. 6 includes a first multiplier circuit 200 and asecond multiplier circuit 202. The X input is applied to the multiplier200, and the Y input is applied to the multiplier 202. The outputs X andY of the two multipliers are applied to a velocity magnitude computationcircuit 204, the output of which is applied to a velocity controlamplifier 206. The multipliers 200 and 202 are described in circuitdetail in FIGS. 8 and 9, the velocity magnitude computation circuit 204is described in FIG. 10, and the velocity control amplifier 206 isdescribed in FIG. 11. The output of the velocity control amplifier 206is introduced to a plurality of gain control buffer amplifiers 208 whoseoutputs GC 1, GC2 and GC3 are fed back to the multiplier circuits 200and 202.

The outputs of the multipliers 200 and 202 also apply to respectiveintegrator circuits 210 and 212 through field effect transistor switchesQ2 and Q8. The X output appears at the output of the integrator circuit210, whereas the Y output appears at the output of the integratorcircuit 212. As in the previous embodiment, the X output is applied tothe X-axis deflection control circuit of the cathode-ray tube, whereasthe Y output is applied to the Y-axis deflection control circuit.

The multiplier circuits 200 and 202 in the X and Y channels of thesystem of FIG. 6 serve as tracking, variable gain elements whichcontinuously adjust the time 204, the velocity control amplifier 206,and the gain control buffer amplifiers 208. This time constant controlloop serves to maintain the X or Y component of spot velocity of thecathode-ray tube constant. The output voltage from the velocitymagnitude component circuit 204 is the magnitude X or Y whichever islarger. At the node of the velocity control amplifier 206, a summingnetwork compares the output of the velocity magnitude computationcontrol circuit 204 with a reference voltage to provide an error signalproportional to the difference. The error signal is integrated by thevelocity control amplifier to provide a gain control voltage to thebuffer amplifiers 208 which feed resulting gain control voltages to themultiplier circuits 200 and 202.

The operation of the time constant control loop is such that if theamplitude of X or Yv decreases because of a decrease in the amplitude ofthe voltage at the multiplier signal input, an error signal at the inputof the velocity control amplifier 206 increases in amplitude and causesa corresponding increz seip the gain control" voltage applied to themultipliers 200 and 202, thereby to increase the amplitude of thevoltages X m, and Ym, towards their normal value.

The vector is drawn from the last end point location held in the vectorintegrator circuits 210 and 212 to a new end point location by firstapplying the new end point signals to the multiplier circuits 200, 202,as designated X INPUT and Y INPUT in FIGS. 6 and 7. The integratorcontrol switches Q2 and OS are closed when the time V BUSY-VG goes truesetting in NVEND and vector generation begins. As the vector is drawn,continuous control of the vector velocity is provided by the gaincontrol circuits until maximum multiplier gain is reached. Vectorvelocity now decreases towards zero on a time constant curve. When theamplitude of the vector velocity signal decreases to approximately 0.5volts, and after a particular time delay, the signal NVEND goes false toopen the switches Q2 and Q8, and to signal the controller that thevector is completed.

The multiplier circuits 200 and 202 are shown in circuit detail in FIGS.8 and 9. FIG. 8 shows the overall circuits, and FIG. 9 shows the circuitdetails of the individual blocks which make up the circuits. As shown inFIG. 8, the X input and Y input are first introduced to respectiveamplifiers, each of which is made up of a pair of transistors Q4 and Q5.The transistor Q4 may be an NPN transistor of the type designated TIS98,and the transistor Q may be a PNP transistor of the type designatedT1893. Each input is applied to the base electrode of the transistor Q4through a 220 ohm resistor R34. The emitter of the transistor 04 isconnected to the base of the transistor 05 through a 220 ohm resistorR35.

The collector of the transistor 04 is connected to the positive terminalof a l5-volt direct voltage source, whereas the collector of thetransistor 05 is connected to the negative terminal of the source. Theemitter of the transistor Q4 is connected to the negative terminalthrough a 33 kilo-ohm resistor R36. The emitter of the transistor O4 inthe X channel is connected to a block designated X1, whereas thetransistor O5 in the Y channel is connected to a block designated Y1.

Two further blocks X2 and X3 are included in the X channel, and the Xoutput appears at the output of the block X3. Likewise, two additionalblocks Y2 and Y3 are included in the Y channel, and the Y output appearsat the output of the block Y3. The circuit details of the blocks X1, X2,X3, Y1, Y2 and Y3may be the same.

As shown in FIG. 9, the individual blocks X1, X2, X3 or Y1, Y2, Y3 mayinclude an integrated circuit designated 1C1, and which may be of thetype presently referred to as SG1595D. The input from the correspondingtransistor Q5 of FIG. 8 is applied through a I kiloohm resistor R1 toone input of the integrated circuit, whereas the corresponding gaincontrol signal is applied to an input terminal of the integratedcircuits through a resistor R10 of, for example, I kilo-ohm. The gaincontrol signal is also applied to the first-mentioned input of theintegrated circuit through a 180 kilo-ohm resistor R31.

The integrated circuit output is amplified in an amplifier A1 which maybe of the type designated 2525, and the output V of each of the blocksof FIG. 8 appears at the output of the amplifier. Appropriate positiveand negative bias potentials are applied to the amplifier Al throughrespective diodes CR3 and CR4. Each of the diodes may be of the typedesignated IN3064. The integrated circuit IC1 and the amplifier A1 areexcited from the aforesaid I5-volt direct voltage source. The positiveterminal of the source is connected through a l kilo-ohm resistor R19and through a pair of diodes CR1 and CR2 to the integrated circuit.These diodes may be of the type designated IN3064. The negative terminalof the source is directly connected to the integrated circuit ICl and tothe amplifier A1.

A 10 kilo-ohm feedback resistor R25 is connected across the amplifierAl. The input terminal V is also connected to a 4.02 kilo-ohm resistorR32 which is shorted by a 10 picofarad capacitor C5. The resistor andcapacitor are connected to the base of a PNP transistor Q2, the emitterof which is connected to the base of a similar transistor Q1. Thetransistors Q1 and Q2 may be PNP transistors of the type designatedTIS93. The collectors of the transistors are grounded. The emitter ofthe transistor Q2 and the base of the transistor Q1 are connected to thepositive terminal of the 15- volt source through a 47 kilo-ohm resistorR20. The base of the transistor O2 is connected to the positive terminalthrough a 2.49 kilo-ohm resistor R21. The resistor R25 is connected tothe positive terminal through a 2.49 kilo-ohm resistor R24.

The gain control signal GCl is applied to the cells X1 and Y1, it hasthe waveform shown in FIG. 7. The gain control signal GC2 is applied tothe cells X2 and Y2, then it has a waveform such as shown in FIG. 7. Thegain control signal GC3 is applied to the cells X3 and Y3, and it has awaveform such as shown in FIG. 7.

The velocity magnitude computation circuit 204 is shown in circuitdetail in FIG. 10. The input X is applied to the cathode of a diode CR21and anode of a diode CR20, whereas the input Y is applied to the anodeof a diode CR22 and cathode of a diode CR23. The anodes of the diodesCR21 and CR23 are connected through a 3.9 kilo-ohm resistor R66 to theposi tive terminal of the 15-volt source, and to the anode of a diodeCR24. The cathodes of the diodes CR20 and CR22 are connected through a10 kilo-ohm resistor R79 to the negative terminal of a 30-volt directvoltage source.

The cathode of the diode CR24 is: connected through a 15 kilo-ohmresistor R80 to the negative terminal of the voltage source, and througha 1.0 kilo-ohm resistor R to the input of an amplifier A3. The otherinput pacitor C15. The resistor R75 is shunted by a picofarad capacitorC17.

The cathode of the diode CR25 is connected back to the cathodes of thediodes CR20 and CR22. The cathode of the diode CR25 is also connected toa 220 ohm resistor R81. The resistor R81 is connected to the base of aPNP transistor Q21, the emitter of which is connected to the collectorof a similar transistor Q20. The transistors Q20 and Q21 may each be ofthe type designated T1893. The collector of the transistor Q21 isdirectly connected to the negative terminal of the l5-volt source, andits emitter is connected to the collector of the transistor Q20.

The emitter of the transistor Q20 is connected through a 270 ohmresistor R69 to the positive terminal of the 15-volt source. The base ofthe transistor Q is connected to the junction of a l kilo-ohm resistorR68 and 2.2 kilo ohm resistor R76. The resistors R68 and R76 areconnected between the positive terminal of the l5-volt source andground. The emitter of the transistor Q21 and collector of thetransistor Q20 are connected to an output terminal which connects withthe input of the velocity control amplifier 206, which is shown incircuit detail in FIG. 11.

The output of the velocity magnitude computation circuit 204 of FIG. 10corresponds to the magnitude of the X or Y input, which ever is thelarger. The diodes CR21 and CR23 supply the larger negative magnitude ofthe two inputs to the inverting amplifier network A3. The diodes CR20and CR22 supply the positive magnitude of the X or Y inputs, whicheveris the larger, to the base of the emitter follower Q21, and the diodeCR25 supplies the inverted negative magnitude to the base of the emitterfollower. Therefore, the output of the circuit of FIG. 10 is themagnitude of the larger velocity input X or Y The velocity controlamplifier 206 receives the out-.

put of the velocity computation circuit 204 through a 4.99 kilo-ohmresistor R89 connected to the input of an amplifier A4. A further 13.3kilo-ohm resistor R88 is connected to the input of the amplifier and tothe negative terminal of the l5-volt source to provide the velocityreference voltage. The other input terminal of the amplifier A4 isgrounded. The first input terminal is also connected to a diode CR34which, in turn, is connected through a 4.7 kilo-ohm resistor R96 to thenegative terminal of the l5-volt source. The anode of the diode CR34 isalso connected to the anode of the Zener diode CR38 which may, forexample, be of the type designated IN756A. The output of the amplifierA4 is connected to the output terminal of the circuit of FIG. 11 througha 1.1 kilo-ohm resistor R104 which is shunted by a 68 picofaradcapacitor C22.

A negative bias is provided for the amplifier through a diode CR38 whichmay be of the type designated CR60. The cathode of the diode is alsoconnected to a grounded 5 picofarad capacitor C21. The amplifier A4 maybe of the type designated 2525. The output of the amplifier is alsoconnected to a 430 ohm resistor R92 which, in turn, is connected to a 10picofarad capacitor C20 and to a 130 picofarad capacitor C42. Thecapacitor C42 is connected to the anode of a diode CR58 and to thecathode ofa diode CR59. The anode of the diode CR59 is connected to thepositive terminal of a 0.7 volt source, and the cathode is connectedthrough a kilo-ohm resistor R to the positive terminal of the l5-voltsource. The cathode of the diode CR58 and the capacitor C20 areconnected to the junction of the resistor R88 and R89.

The input to the velocity control amplifier 206 of FIG. 1 l is the errorsignal between the actual X and Y velocity signal magnitude and theaforesaid reference voltage. The resistor R88 supplies the reference tothe input of the amplifier R84, and the resistor R89 supplies the actualsignal magnitude. The components R92, C42, C20 are included in anintegrating network which is connected around the amplifier A4 forstability of the loop. A fast set-up circuit consisting of the diodesCR58 and CR59 and the resistor R175 is used to decrease the velocityloop settling time by increasing the charge current to the capacitor C42for decreasing the multiplier gain.

The output of the velocity control amplifier 206 is fed to threedifferential gain control buffer amplifiers, as represented by the block208 in FIG. 6. These buffer amplifiers respectively supply the gaincontrol voltages GCl, GC2 and GC3 to the multiplier circuits 200 and202. The differential gain control buffer amplifiers have an outputrange, limited, for example, to plus or minus 4-volts. The negativeinputs of all the gain control amplifiers are connected together buttheir positive inputs are biased to levels 0.2 volts apart. Therefore,only one of the gain control buffer amplifiers is active at a time,while the outputs of the other two buffer amplifiers are clamped at i 4volts, as shown in FIG. 7.

The system of FIG. 6 functions, therefore, in a manner similar to thepreviously described system of FIG. 4. However, in the system of FIG. 6,the time constant, instead of being changed at discrete points, as isthe case with the system of FIG. 4 and as shown in FIG. 5, is changedcontinuously as each vector is drawn.

The invention provides, therefore, an improved system whereby a vectormay be displayed accurately and precisely, and by means of relativelyinexpensive control circuitry. Moreover, the system described herein iscontrolled so that the vector is drawn at optimum speed during alloperational conditions.

It will be appreciated, of course, that although particular embodimentsof the invention have been shown and described, modifications may bemade. It is intended to cover in the following claims all suchmodifications which come within the spirit and scope of the invention.

What is claimed is:

1. A system for generating X-axis and Y-axis vector signals including incombination: first circuitry responsive to an applied input signal forgenerating an exponential X-axis analog output signal in accordance withthe relationship [X Y(t) (X X,) 6"", where T is the time constant;second circuitry responsive to an applied input signal for generating anexponential Y- axis analog output signal in accordance with therelationship [Y Y(t) (Y, Y,) e'"; and utilization means for said X-axisand Y-axis exponential analog signals, said utilization means comprisinga scanning element, X-axis and Y-axis deflection means for deflectingthe scanning element, and X-axis and Y-axis deflection control circuitryrespectively coupled to said X-axis and Y-axis deflection means and tosaid first and second circuitry for causing said scanning element toscan along a linear path between a starting point and an end point torepresent a particular vector as established by the input signals.

2. The combination defined in claim 1, in which the parameters of saidfirst and second circuitry are such that the time constant (T) of theX-axis exponential analog output signal of said first circuitry is thesame as the time constant (T) of said Y-axis exponential analog outputsignal of said second circuitry.

3. The combination defined in claim 1, in which said first circuitry andsaid second circuitry each includes an integrating operational amplifiercircuit.

4. The combination defined in claim 1, in which said input signal tosaid first circuitry and to said second circuitry each comprises a stepfunction corresponding to the coordinates of a predetermined startingpoint and end point.

5. The combination defined in claim 1, in which said first circuitry andsaid second circuitry each includes a switching network for establishingan end point when the analog output signals of said first and secondcircuitry reach a predetermined minimum value.

6. The system defined in claim 1, in which said utilization meanscomprises a cathode-ray tube having a viewing screen, means forproducing a cathode-ray beam within the tube, X-axis and Y-axisdeflection means for deflecting the beam across the screen, and X-axisand Y-axis deflection control circuitry respectively coupled to saidXaxis and Y-axis deflection means, said control circuitry beingresponsive to applied analog signals for causing the cathode-ray beam toscan cyclically across said screen between a starting point and an endpoint to represent a particular vector as established by said appliedanalog signals; and in which said first and second circuitry areincluded respectively in said X-axis and Y-axis control circuitry.

7. The combination defined in claim 2, and which includes controlcircuitry for simultaneously changing said time constants as theamplitude levels of said output signals change.

8. The combination defined in claim 7, in which said control circuitryincludes switching means responsive to preestablished amplitude levelsof said output signals simultaneously to change the time constantsthereof.

9. The combination defined in claim 7, in which said control circuitryincludes network means responsive to the output amplitudes of saidoutput signals simultaneously to change the time constants thereof on acontinuous basis.

1. A system for generating X-axis and Y-axis vector signals including incombination: first circuitry responsive to an applied input signal forgenerating an exponential X-axis analog output signal in accordance withthe relationship (X2 - Y(t) ) (X2 - X1) e t/T, where T is the timeconstant; second circuitry responsive to an applied input signal forgenerating an exponential Y-axis analog output signal in accordance withthe relationship (Y2 - Y(t) ) (Y2 - Y1) e t/T; and utilization means forsaid X-axis and Y-axis exponential analog signals, said utilizationmeans cOmprising a scanning element, X-axis and Yaxis deflection meansfor deflecting the scanning element, and Xaxis and Y-axis deflectioncontrol circuitry respectively coupled to said X-axis and Y-axisdeflection means and to said first and second circuitry for causing saidscanning element to scan along a linear path between a starting pointand an end point to represent a particular vector as established by theinput signals.
 2. The combination defined in claim 1, in which theparameters of said first and second circuitry are such that the timeconstant (T) of the X-axis exponential analog output signal of saidfirst circuitry is the same as the time constant (T) of said Y-axisexponential analog output signal of said second circuitry.
 3. Thecombination defined in claim 1, in which said first circuitry and saidsecond circuitry each includes an integrating operational amplifiercircuit.
 4. The combination defined in claim 1, in which said inputsignal to said first circuitry and to said second circuitry eachcomprises a step function corresponding to the coordinates of apredetermined starting point and end point.
 5. The combination definedin claim 1, in which said first circuitry and said second circuitry eachincludes a switching network for establishing an end point when theanalog output signals of said first and second circuitry reach apredetermined minimum value.
 6. The system defined in claim 1, in whichsaid utilization means comprises a cathode-ray tube having a viewingscreen, means for producing a cathode-ray beam within the tube, X-axisand Y-axis deflection means for deflecting the beam across the screen,and X-axis and Y-axis deflection control circuitry respectively coupledto said X-axis and Y-axis deflection means, said control circuitry beingresponsive to applied analog signals for causing the cathode-ray beam toscan cyclically across said screen between a starting point and an endpoint to represent a particular vector as established by said appliedanalog signals; and in which said first and second circuitry areincluded respectively in said X-axis and Y-axis control circuitry. 7.The combination defined in claim 2, and which includes control circuitryfor simultaneously changing said time constants as the amplitude levelsof said output signals change.
 8. The combination defined in claim 7, inwhich said control circuitry includes switching means responsive topreestablished amplitude levels of said output signals simultaneously tochange the time constants thereof.
 9. The combination defined in claim7, in which said control circuitry includes network means responsive tothe output amplitudes of said output signals simultaneously to changethe time constants thereof on a continuous basis.